Revision Notes
Past Papers
All Videos
Topical Questions
Paper Analysis
Year-Wise Papers
Mathematics - Additional - 0606 - Concept Videos
Access clear, step-by-step explanations to Learn Smarter and Faster.
All Topics
10:00
Representing vectors in different forms: Directed line segment notation AB→
10:00
Representing vectors in different forms: Component notation ai + bj
10:00
Understanding and using vector notation
10:00
Representing vectors in different forms: Column notation [a, b]
10:00
Understanding position vectors
10:00
Finding the unit vector in a given direction
10:00
Finding the magnitude of a vector
10:00
Adding and subtracting vectors
10:00
Multiplying vectors by scalars
10:00
Equating like vectors and solving vector equations
10:00
Determining a resultant vector by adding two or more vectors
10:00
Using velocity vectors to determine position
10:00
Solving real-world problems involving vector motion, such as particle collisions
10:00
Finding the equation of a common chord
10:00
Determining whether two circles intersect
10:00
Determining whether two circles touch externally or internally
10:00
Determining whether two circles do not intersect
10:00
Finding points of intersection between two circles
10:00
Understanding and using the equation of a circle with center (a, b) and radius r
10:00
Identifying the center and radius from different forms of a circle equation
10:00
Example: (x - a)^2 + (y - b)^2 = r^2
10:00
Example: x^2 + y^2 + 2gx + 2fy + c = 0
10:00
Finding points of intersection between a circle and a straight line
10:00
Determining whether a line is a tangent
10:00
Determining whether a line is a chord
10:00
Determining whether a line does not intersect the circle
10:00
Finding the equation of a tangent to a circle at a given point
10:00
Understanding properties of tangents (no calculus required)
10:00
Example: 3e^x = 12 - 5e^{-x}
10:00
Using substitution to form and solve a quadratic equation
10:00
Example: x^4 - 3x^2 + 1 = 0
10:00
Example: 2(ln 5x)^2 + ln 5x - 6 = 0
10:00
Sketching cubic polynomial graphs given in factorized form
10:00
Sketching the modulus of cubic polynomials
10:00
Identifying points of intersection with the coordinate axes
10:00
Solving inequalities graphically for cubic functions of the form: f(x) ≥ d
10:00
Solving inequalities graphically for cubic functions of the form: f(x) > d
10:00
Solving inequalities graphically for cubic functions of the form: f(x) ≤ d
10:00
Solving inequalities graphically for cubic functions of the form: f(x) < d
10:00
Solving |ax + b| = c (for c ≥ 0)
10:00
Solving |ax + b| = cx + d
10:00
Solving |ax + b| = |cx + d|
10:00
Solving |ax^2 + bx + c| = d using algebraic or graphical methods
10:00
Solving k|ax + b| > c and k|ax + b| ≤ c (for c > 0)
10:00
Solving k|ax + b| ≤ |cx + d|, where k > 0
10:00
Solving |ax + b| ≤ cx + d
10:00
Solving |ax^2 + bx + c| > d and |ax^2 + bx + c| ≤ d
10:00
Function, domain, range (image set)
10:00
One–one function, many–one function
10:00
Inverse function and composition of functions
10:00
Finding the domain and range of functions
10:00
Domain restrictions for inverse functions and composite functions
10:00
Recognising and using function notation
10:00
Examples: f(x) = 2e^x, f : x ↦ log x, f^(-1)(x), fg(x), f^2(x)
10:00
Relationship between y = f(x) and y = |f(x)|
10:00
Cases of linear, quadratic, cubic, and trigonometric functions
10:00
Understanding why a function does not have an inverse
10:00
Finding the inverse of a one–one function
10:00
Formation and usage of composite functions
10:00
Understanding order dependency in composite functions
10:00
Sketching the relationship between a function and its inverse
10:00
Reflection along the line y = x
10:00
Understanding and applying radian measure
10:00
Calculating arc length using the formula s = rθ
10:00
Calculating sector area using the formula A = (1/2) r^2 θ
10:00
Solving problems involving arc length and sector area, including compound shapes
10:00
Understanding and using the six trigonometric functions: sine, cosine, tangent, secant, cosecant, an
10:00
Understanding and using amplitude and period of trigonometric functions
10:00
Relationship between graphs of related trigonometric functions
10:00
Graphing y = a sin(bx) + c, y = a cos(bx) + c, y = a tan(bx) + c
10:00
Identifying period and amplitude in the graphs
10:00
Labeling asymptotes for the tangent function
10:00
Using the fundamental identities: sin^2 A + cos^2 A = 1
10:00
Using the fundamental identities: sec^2 A = 1 + tan^2 A
10:00
Using the fundamental identities: csc^2 A = 1 + cot^2 A
10:00
Solving equations involving the six trigonometric functions within a given domain
10:00
Using trigonometric identities to simplify and solve equations
10:00
Proving trigonometric identities using algebraic manipulation and identities
10:00
Solving simultaneous equations in two unknowns using elimination or substitution
10:00
Example: y - x + 3 = 0 and x^2 - 3xy + y^2 + 19 = 0
10:00
Example: xy^2 = 4 and xy = 3
10:00
Example: (y/x) + (x/y^2) = 4 and y = x - 2
10:00
Understanding the concept of a derivative
10:00
Notation for differentiation: f'(x), dy/dx, d^2y/dx^2
10:00
Differentiating standard functions: x^n (for any rational n), sin x, cos x, tan x, e^x, ln x
10:00
Using constant multiples, sums, and the chain rule
10:00
Differentiating products of functions using the product rule
10:00
Differentiating quotients of functions using the quotient rule
10:00
Finding gradients, tangents, and normals to curves
10:00
Finding stationary points (maxima and minima)
10:00
Using first and second derivative tests to classify stationary points
10:00
Applying differentiation to connected rates of change problems
10:00
Using small increments for approximations
10:00
Understanding integration as the reverse of differentiation
10:00
Notation and the inclusion of an arbitrary constant
10:00
Integrating sums of terms in powers of x
10:00
Integrating functions of the form: (ax + b)^n, sin(ax + b), cos(ax + b), sec^2(ax + b), e^(ax+b)
10:00
Evaluating definite integrals
10:00
Finding areas between curves and the x-axis
10:00
Using differentiation and integration in kinematics
10:00
Drawing and interpreting displacement-time, velocity-time, and acceleration-time graphs
10:00
Understanding and using properties of logarithmic and exponential functions, including ln x and e^x
10:00
Recognizing that f(x) = e^x and g(x) = ln x are inverse functions
10:00
Understanding the asymptotic nature of logarithmic and exponential graphs
10:00
Identifying equations of asymptotes
10:00
Applying the laws of logarithms, including change of base
10:00
Example: Expressing 3 + log p - log q as a single logarithm
10:00
Example: Converting log_e(1/5) to natural logarithm notation
10:00
Solving equations of the form a^x = b using logarithms
10:00
Finding the maximum or minimum value by completing the square or by differentiation
10:00
Using the maximum or minimum value to sketch the graph
10:00
Determining the range for a given domain
10:00
Two real roots condition
10:00
Two equal roots condition
10:00
No real roots condition
10:00
Related conditions for intersection, tangency, or no intersection of a line with a curve
10:00
Methods: Factorisation, quadratic formula, and completing the square
10:00
Finding solution sets graphically or algebraically
10:00
Writing solutions in the correct form (e.g., -3 < x < 4, x < 1 or x > 6)
10:00
Understanding and using the equation of a straight line in the form y = mx + c
10:00
Conditions for two lines to be parallel
10:00
Conditions for two lines to be perpendicular
10:00
Calculating the midpoint of a line segment
10:00
Finding the length of a line segment
10:00
Finding and using the equation of a perpendicular bisector
10:00
Transforming non-linear relationships into straight-line form
10:00
Determining unknown constants using gradient or intercept of transformed graph
10:00
Example: Converting equations such as y = Ax^n and y = Ab^x into straight-line form
10:00
Example: Transforming equations to the form y^2 = Ax^3 + B, e^{2y} = Ax^2 + B, y^3 = A ln x + B
10:00
Recognizing the difference between permutations and combinations
10:00
Knowing when to use permutations versus combinations
10:00
Understanding and using factorial notation n!
10:00
Applying formulas for permutations and combinations of n items taken r at a time
10:00
Solving real-world problems using permutations and combinations
10:00
Understanding restrictions such as repetition of objects, circular arrangements, and mixed cases
10:00
Understanding and using the remainder theorem
10:00
Understanding and using the factor theorem
10:00
Finding factors of polynomials using algebraic long division
10:00
Finding factors by observation
10:00
Solving cubic equations by factorization and algebraic manipulation
10:00
Expanding (a + b)^n for positive integer n using the binomial theorem
10:00
Simplifying coefficients in binomial expansions
10:00
Using the general term formula: T_r = (nCr) a^(n-r) b^r
10:00
Finding specific terms in binomial expansions
10:00
Finding terms independent of x in an expansion
10:00
Recognizing arithmetic and geometric progressions
10:00
Understanding the difference between arithmetic and geometric progressions
10:00
Using formulas for nth term of an arithmetic progression
10:00
Using formulas for sum of the first n terms of an arithmetic progression
10:00
Using formulas for nth term of a geometric progression
10:00
Using formulas for sum of the first n terms of a geometric progression
10:00
Understanding the condition for convergence of a geometric progression
10:00
